Dynamic tuning of enhanced intrinsic circular dichroism in plasmonic stereo-metamoleculearray with surface lattice resonance

Liu, Shao-Ding; Liu, Jun-Yan; Cao, Zhaolong; Fan, Jin-Li; Lei, Dangyuan

Published in:Nanophotonics

Published: 01/09/2020

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Published version (DOI):10.1515/nanoph-2020-0130

Publication details:Liu, S-D., Liu, J-Y., Cao, Z., Fan, J-L., & Lei, D. (2020). Dynamic tuning of enhanced intrinsic circular dichroismin plasmonic stereo-metamolecule array with surface lattice resonance. Nanophotonics, 9(10), 3419–3434.https://doi.org/10.1515/nanoph-2020-0130

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Download date: 12/07/2021

Research article

Shao-Ding Liu*, Jun-Yan Liu, Zhaolong Cao, Jin-Li Fan and Dangyuan Lei*

Dynamic tuning of enhanced intrinsic circulardichroism in plasmonic stereo-metamoleculearray with surface lattice resonancehttps://doi.org/10.1515/nanoph-2020-0130Received February 18, 2020; accepted April 6, 2020; published onlineMay 14, 2020

Abstract: Enhancing the circular dichroism signals ofchiral plasmonic nanostructures is vital for realizingminiaturized functional chiroptical devices, such as ul-trathin wave plates and high-performance chiral bio-sensors. Rationally assembling individual plasmonicmetamolecules into coupled nanoclusters or periodic ar-rays provides an extra degree of freedom to effectivelymanipulate and leverage the intrinsic circular dichroism ofthe constituent structures. Here, we show that sophisti-cated manipulation over the geometric parameters of aplasmonic stereo-metamolecule array enables selectiveexcitation of its surface lattice resonance mode either byleft- or right-handed circularly polarized incidence throughdiffraction coupling, which can significantly amplify thedifferential absorption and hence the intrinsic circular di-chroism. In particular, since the diffraction coupling re-quires no index-matching condition and its handednesscan be switched by manipulating the refractive index ofeither the superstrate or the substrate, it is therefore

possible to achieve dynamic tuning and active control ofthe intrinsic circular dichroism response without the needof modifying structure parameters. Our proposed systemprovides a versatile platform for ultrasensitive chiralplasmonics biosensing and light field manipulation.

Keywords: chiral plasmonics; circular dichroism; plasmonhybridization; plasmonic metamolecule; surface latticeresonance.

1 Introduction

Circular dichroism (CD) characterized by the differential ab-sorption of left-handed (LCP) and right-handed circularlypolarized (RCP) light is an intrinsic property of chiral com-pounds, which provides a powerful spectroscopy tool forstructural and conformational analyses of complex bio-molecules [1, 2]. However, the CD signals of naturally occurringmaterials are typically very weak due to their small dipolemoments and hence a weak coupling with the incident light,and therefore can be detectable only at high concentrations orlarge volumes. This constitutes a significant long-standingobstacle for realizingcompact chiropticalnanophotonicdeviceswith naturally occurring chiral compounds, and has sparked aconsiderable amount of research interests in designing artificialman-made structures with enhanced CD signals [3–8].

Over the past decade, the extraordinary CD responsesof plasmonic chiral nanostructures have gained consider-able attention, where the excitation of localized surfaceplasmon resonances (LSPRs) significantly enhances thelight-structure interaction strength due to their extremelylarge dipole moments, and the generated CD signals arethus orders of magnitude larger than that of natural com-pounds [9–17]. Such enhanced plasmonic chirality is alsofeatured with flexible modulation of both CD resonancemagnitude and frequency through manipulating thestructural geometry and constituents [4, 18, 19]. Thus far,strong intrinsic CD responses have been observed in three-dimensional plasmonic helixes [20–30], spirals [31–33],nanopillars [34], twisted nanoparticles (e. g., split-ringresonators (SRRs) [35, 36], gammadions [37], arcs [38], and

*Corresponding authors: Shao-Ding Liu, Key Lab of AdvancedTransducers and Intelligent Control System of Ministry of Education,Taiyuan University of Technology, Taiyuan, 030024, PR China; andDepartment of Physics and Optoelectronics, Taiyuan University ofTechnology, Taiyuan, 030024, PR China,E-mail: liushaoding@tyut.edu.cn, https://orcid.org/0000-0003-4809-9815; Dangyuan Lei, Department of Materials Science andEngineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon,Hong Kong, E-mail: dangylei@cityu.edu.hk, https://orcid.org/0000-0002-8963-0193Jun-Yan Liu and Jin-Li Fan: Key Lab of Advanced Transducers andIntelligent Control System ofMinistry of Education, Taiyuan Universityof Technology, Taiyuan, 030024, PR China; Department of Physics andOptoelectronics, Taiyuan University of Technology, Taiyuan, 030024,PR ChinaZhaolong Cao: State Key Laboratory of Optoelectronic Materials andTechnologies and Guangdong Province Key Laboratory of DisplayMaterial and Technology, School of Physics and Engineering, Sun Yat-sen University, Guangzhou, 510275, PR China

Nanophotonics 2020; 9(10): 3419–3434

Open Access. © 2020 Shao-Ding Liu et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0International License.

rods [11, 39–43]), and oligomer clusters [44–54]. Evenhanded planar structures exhibit remarkable CD despitethe fact that they are not truly chiral [55–66], and theirchiral responses can be strongly enhanced with the for-mation of Fano resonances [66, 67], which are promisingplatforms to manipulate chiral light-matter interactions atthe nanoscale [68]. More interestingly, the CD resonancefrequency and strength can be controlled by photoinducedoptical handedness switching effects [69], phase-changingmaterials [70, 71], external magnetic fields [72], excitationpower [73], and (DNA) origami templates [74–83], whichpave the way for realizing chiroptically active devices.

Recently, plasmonic chiral metasurfaces consist ofmetallic nanostructures organized in C4 symmetry hasbeen demonstrated to exhibit intrinsic CD responseswithout invoking the birefringence effect [11, 48–51]. Undersuch symmetrical arrangement, the metasurfaces CD re-sponses are definitely characterized by the differentialtransmission of LCP and RCP incidences, which is identicalto that of the differential absorption. In analogy to molec-ular physics, the constituent nanostructures in such met-asurfaces can be termed artificial plasmonic “molecules”[84, 85]. Essentially, the transmission CD signals of thechiral metasurfaces with C4 symmetry are governed by thedifferential absorption cross section of constituent plas-monic “molecules.” However, the absorption cross sectionof a single plasmonic “molecule” cannot be increasedsignificantly by simply increasing its structural sizecompared with that of its scattering [86], and the differ-ential absorption of the plasmonic “molecule” is thereforerelatively weak. As a result, very dense arrays of chiralnanostructures are used to enlarge the transmission CDmagnitude. In this case, the absorption of the matchedcircularly polarized incidence can be enhanced, but theabsorption of the opposite circularly polarized incidencethat intends to be transmitted is enhanced simultaneously.This obstacle would be more obvious when plasmon res-onances shift to the visible and near-infrared frequencies.For example, the transmission CD magnitude can be aslarge as 0.4 for a very dense stereo-metamaterial composedof twisted SRR dimers in the near-infrared spectral range[87–92], but themagnitude is less than 0.1 for a sparse arraymade of similar constituent structures [93]. Although theCD response for a similar stereo-metamaterial designed bya deep learning method can be enlarged to about 0.8 [94],the light transmission is blocked due to the presence of agold film mirror in the structure, and the birefringence ef-fect is also involved in the CD response.

In addition to single plasmonic “molecules,” theplasmonic responses of metal nanoparticle arrays aregoverned by surface propagating modes caused by the

electromagnetic coupling between unit cells, e. g.,extraordinary optical transmission (EOT) related to sur-face plasmon polaritons [95], and surface lattice reso-nance (SLR) modes caused by diffraction couplingbetween LSPRs and Rayleigh anomalies (RAs) [96–100].Radiative losses can be effectively suppressed with theexcitation of SLR modes, which leads to sharp reso-nances with large Q-factors [101–103]. What's moreimportant is that the optical interaction between thenanoparticles and the incident field can be enhanced bythe surface propagating modes, and the absorption ofnanoparticle arrays can hence be strongly amplified[104]. This indicates that the coupling between the con-stituent structures in plasmonic arrays be possibly usedfor enhancing the CD responses. Several pioneer workshave demonstrated the CD responses of planar plasmonicnanostructure arrays associated with the excitations ofsurface propagating modes. Maoz et al. and Wang et al.have reported respectively the enhanced CD in plasmonicnanohole arrayswith the EOT effect [105, 106], and the CDresponses can also be tuned by adjusting the arrayperiod. It has been demonstrated a large differentialtransmission for LCP and RCP incidences in achiralnanoparticle arrays with the excitation of two differentSLRs [107, 108], and Cotrufo et al. have shown that thesurface lattice resonance in a handed planar rod arrayplays an important role in determining the spin-depen-dent emission of light [109]. Nevertheless, these struc-tures are not truly chiral, and the CD responses arerelated to their extrinsic chirality. Besides that, theexcitation of the SLR modes in those structures requiresto fulfill the index-matching conditions, the enhanced CDfor the SRR arrays can only be observed under obliqueincidences [107, 108], and the CD magnitude for thenanohole arrays is still relatively weak [105, 106].

In this work, we investigate the chiroptical responseof a plasmonic stereo-metamolecule array and show thatthe CD resonance strength can be significantly leveragedby selectively exciting SLRmodes. Although the intrinsicdifferential absorption of the constituent stereo-meta-molecules is quite weak, their periodic counterpart ex-hibits an SLR-enhanced CD signal of up to 0.7, which isabout 6 times larger than that without diffractioncoupling. This observation can be explained within theframework of a modified plasmonic Born–Kuhn model.Moreover, since the enhanced CD does not rely on index-matching conditions, it is therefore possible to realizedynamic tuning or active control of the chiropticalresponse without modifying the structure geometry.Our results highlight the robustness and significanceof achiral SLR in chirality enhancement, which can

3420 S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism

be a general scheme for a wide range of chiral meta-material designs such as stereo-SRR dimers and olig-omer clusters.

2 Results and discussion

2.1 CD of single stereo-SRR dimers

Figure 1a illustrates the configuration and geometricparameters of a gold stereo-SRR dimerwith the upper SRRrotated clockwise by an angle θwith respect to the y-axis.Here, the horizontal displacement d between the twoSRRs is intentionally introduced to enhance near-fieldcoupling at the gap area [88–92], and the verticaldisplacement s can be used to manipulate the couplingand the phase retardation. Depending on the relativeposition and twist angle, the SRR dimer can be left-handed (L-Enantiomer) or right-handed (D-Enantiomer).The spacer layer (e. g., solidfiable photopolymer, PC403)is supposed to have the same refractive index as the silicasubstrate (nsilica = nspacer = 1.50), while the superstrate

material is set to be air (nsup = 1.00). When circularlypolarized light is incident normally onto the structurefrom the air side, plasmonic coupling between the elec-tric dipole mode of the upper SRR and the quadrupolemode of the lower one results in the formation of hy-bridized bonding dipole-quadrupole (BDQ) and anti-bonding dipole-quadrupole (ABDQ) resonance modes(Figure 1b) [84, 85]. Plasmon hybridization between twoelectric dipolemodes of the dimer is neglected here due totheir significant phase mismatch. More detailed infor-mation can be found in Figure S1. Such hybridizationmodes can be selectively excited by RCP and LCP in-cidences, depending on the phase retardation betweenthe two SRRs. As a result, the difference in excitationefficiency of the two circular polarized incidences is ex-pected to generate CD signals around the resonance fre-quency of the SRR dimer.

The absorption cross-section (Abs) spectra of the sin-gle modified stereo-SRR dimer (D-Enantiomer) under RCPand LCP incidences are shown in the upper panel ofFigure 2a. As expected from our qualitative reasoning, theRCP mode is located at a lower energy (990 nm), which

Figure 1: Geometric configuration andplasmon hybridization of a modified goldstereo-SRR dimer. (a) Schematic views ofthe modified stereo-SRR dimer, showinggeometric parameters such as ring radiusr = 90 nm, width w = 40 nm, gap widthg = 30 nm, thickness h = 40 nm, verticalseparation s=60 nm, horizontal separationd = 90 nm and twisted angle θ = 60°. Therefractive index of the substratensub = nsilica = nspacer = 1.50, and thesuperstrate nsup = 1.00. (b) Plasmonhybridization between the electric dipoleand quadrupole modes in a D-Enantiomer,forming an antibonding dipole-quadrupole(ABDQ) and a bonding dipole-quadrupole(BDQ) resonance.

S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism 3421

corresponds to the bonding mode (BDQ), whereas the LCPmode lies at a higher energy (880 nm), corresponding tothe antibonding mode (ABDQ). In addition, the resonanceshoulder around 1100 nm under the LCP incidence isattributed to the excitation of a hybridized dipole mode(Figure S1). As a result, a positive differential absorption(ΔAbs = AbsLCP – AbsRCP) peak occurs at 880 nm and anegative one at 987 nm as shown in the lower panel ofFigure 2a, leading to the CD response of the stereo-SRRdimer. The corresponding near-field and surface chargedistribution profiles at the two CD peaks are rendered inFigure 2b,c, respectively. Clearly, the surface charge pro-files confirm the electric dipole mode of the upper ring andthe quadrupole mode of the lower ring at their resonancewavelengths. However, there is a π phase difference for thequadrupole mode of the lower ring at the two resonances,confirming our analysis of hybridized ABDQ and BDQmodes.

2.2 Enhanced CD with surface latticeresonances

In order to highlight the importance of SLR in enhancingplasmonic chiroptical effects, we arrange chiral stereo-SRR dimers in a C4-symmetric supercell to avoid circularbirefringence (Figure 3a). The supercell has a periodp = 890 nm and the center-to-center distance between twoadjacent dimers is 450 nm. The simulated transmission andabsorption spectra of the array under RCP and LCP in-cidences as well as the corresponding transmission CDspectrum are plotted in Figure 3b. An ensemble CD spec-trum by assuming no coupling between adjacent dimers isalso overlaid as a dotted line for comparison. One canimmediately see two pronounced positive and negative CDpeaks at 831 and 949 nm for the array, both blue-shiftedcompared to the reference spectrum. This can be attributedto the effective mode volume overlapping between SRR

Figure 2: CD response of a single modifiedgold stereo-SRR dimer. (a) Absorptioncross-section spectra of a singleD-Enantiomer under LCP and RCPincidences (upper panel) andcorresponding differential absorption(ΔAbs) spectrum, i. e., CD spectrum (lowerpanel). (b, c) Near-field enhancement (|E/E0|, left panels) and surface charge (rightpanels) distribution profiles at the ABDQ (b)and (c) BDQ resonance wavelengths.

3422 S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism

dimers in the array (Figure S2 in Supporting Information).The positive CD peak increases slightly comparedwith thatof the single dimer (red circle), while the negative CD peakat 949 nm (blue solid circle) is enhanced to 0.70, which is 6times larger than the ensemble CD spectrum. This is a clearevidence that electromagnetic coupling between adjacentdimers plays an important role in the chiroptical signalenhancement. In fact, it has recently been demonstratedthat the coupling between a localized plasmon resonanceand the Bragg resonance of a periodic lattice be used toimprove the resonance quality factor and light absorption[110]. It should be noted fromFigure 3b that there is anotherresonance peak located at 1078 nm, which is the bonding

dipole-dipole (BDD) mode of the chiral stereo-SRR, whosenear-field and surface charge distribution profiles can befound in Figure S3.

The above observation of enhanced CD in the array ofC4-arranged chiral stereo-SRR dimers can be attributed tothe emergence of SLRmodes due to collective oscillation ofLSPRs in each unit cell. In short, for a periodic plasmonicnanoparticle array, Rayleigh anomalies that are associatedwith light diffracted parallel to the array surface, occurat [96–99],

λ(i,j)med� p × nmed�����

i2 + j2√ (1)

where nmed is either the refractive index of the superstrate(nsup) or the substrate (nsub), and (i, j)med denotes thediffraction order. When the incident angle is just acrossRAs at a plasmon resonance band, the unit cellsdiffractively couple to each other, creating a propagatingSLR mode. The spectral positions of relevant RAs aredenoted by the gray dashed lines in Figure 3b. As a result,plasmonic non-radiative absorption is increased by theenhanced interaction between incident field and lossymetal but plasmonic radiative scattering is suppressed dueto diffraction coupling, leading to an overall sharpresonance peak with high Q-factor [104]. Therefore, theabsorption of a chiral plasmonic nanostructure array isexpected to be greatly enhanced under an appropriatecircularly polarized incidence but negligible for theopposite one, leading to a pronounced CD peak. It isworth to emphasize that, although the refractive indexes ofthe superstrate and substrate are not equal (nsub = 1.50,nsup = 1.00), the index-matching condition here is not anecessary requirement to realize strongly enhanced CDresponse.

The sharp resonance and CD peak located at 949 nm(blue solid circle) occurs on the long-wavelength side of the(1, 0)sup RA (please note that to simplify the expression, therest degenerate RAs in Figure 3b are not indicated here),and the resonance quality factor is larger than that of thelocalized resonances shown in Figure 2a, which are thesignatures of coupling light into SLR mode [104]. Besidesthat, the near-field distributions shown in Figure S4demonstrate that there are relatively strong field en-hancements between the unit cells, and propagatingwavesare observed along both x- and y-directions, which furtherreveal the excitation of the SLR. The corresponding fieldpattern for a single stereo-SRR in the unit cell (Figure 4) isconsistent with Figure 2c, demonstrating that, indeed, it isthe BDQ mode. As expected, the excitation efficiency ofBDQ mode inherits from its single structure situation. This

Figure 3: CD responses of a stereo-SRR dimer array organized in C4symmetry. (a) Schematic views of the stereo-SRRdimer array. (b) Thetransmission (upper panel) and absorption (middle panel) spectrawith RCP (blue lines) and LCP (red lines) incidences, and thecorresponding CD in transmission of the array (solid line, lowerpanel). The dotted line in lower panel is calculated from equationΔT = 4 × ΔAbs/p2, which is the ensemble average of CD responsecalculated by neglecting the coupling between dimers. The verticaldashed lines denote the spectral positions of corresponding RAs,and the tick labels on the right side represent the converted crosssection values by multiplying the area of the unit cell (p2).

S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism 3423

behavior is also confirmed in Figure 4b where near-field isgreatly enhanced. In this case, the BDQ mode is efficientlyexcited by RCP incidence, giving rise to enhanced ab-sorption (Abs ∼ 0.84), whereas LCP illumination stands onthe opposite side with negligible absorption (Abs ∼ 0.14). Itshould be noted that although the (1, 1)sub RA in the sub-strate is around the same spectral range, it is almostoverlapped with the maximum point of the sharp reso-nance. This behavior does not satisfy the relation betweenan RA and SLR mode, and it should not be the maincontribution of the enhancement. This can also be verifiedin Figure 4b that the field enhancement around the upperrings are stronger than that of the lower ones, demon-strating that the SLR is caused by the diffraction couplingof the BDQ mode in the superstrate. Actually, the (1, 1)subRA mostly interacts with the BDD mode at 1078 nm(Figure S3) and is beyond the scope of this study. Wetherefore dismiss the (1, 1)sub SLR hereafter throughout thispaper.

The broad resonance peak at 831 nm is attributed to theABDQmode (Figure 4a), and interestingly, exhibitingweakchiroptical enhancement (Figure 3b). This is from the factthat, the ABDQ mode is located, on one hand, at the short-wavelength side of (1, 0)sup RA, thus no (1, 0)sup SLRresonance, and on the other hand far away from (2, 0)supRA, yielding weak diffraction coupling. As a result, chiralstereo-SRR dimer arrays at this band restore to uncoupledsituation, where the corresponding CD signal is compara-ble to that of ensemble CD spectrum. This phenomenon canbe confirmed in Figure 4a where the near-field enhance-ment is also comparable with that of the single dimer(Figure 2b). Another example sharing the samemechanismis the hybridized magnetic dipole-dipole mode centeredat 2100 nm. As shown in Figure 5 and Figure S5, theCD response of the stereo-SRR dimer array appears inits magnetic dipole-dipole coupling range. When the

magnetic resonance wavelength is far away from the RAs,there is no diffraction coupling between unit cells. As aresult, the CD response of the array is almost identical tothat for an ensemble of the same number of single SRRdimers without diffraction coupling (lower panel,Figure 5). The maximum CD in transmission is only about0.12, and it is in accordance with the experimental resultsreported in previous studies [93]. Considering that themagnitude of differential absorption cross sections for thehybridized magnetic dipole resonances are comparablewith that of the ABDQ and BDQ modes (Figures 2 and S4),the excitation of SLRs can be an effective approach forenhancing the intrinsic CD responses.

Figure 4: Near-field enhancement (leftpanels) and charge distribution (rightpanels) of one dimer in the supercell arrayat the positive and negative CD peaksshown in Figure 3, where the ABDQ (a) andBDQ (b) modes are excited. BDQ mode aregreatly enhanced compared with singledimer situation due to the diffractioncoupling.

Figure 5: CD responses related to the magnetic dipole resonance ofthe stereo-SRR dimer array shown in Figure 3. Upper panel:transmission spectra under RCP (blue lines) and LCP (red lines)incidences; Lower panel: corresponding transmission CD spectrumfor the dimer array (solid line) and the CD spectrum calculated for anensemble of uncoupled single dimers (ΔT = 4 × ΔAbs/p2, dotted line).

3424 S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism

2.3 Optimized condition for enhanced CD

SLRs and LSPRs are two resonance modes that stem fromdistinct physical mechanisms. In other words, SLRs is acollective resonance mode with high Q-factors and can bemanipulated by tuning the period of the arrays. In contrast,LSPRs solely depends on the property of metamolecules.Therefore, one is able to tune the two resonances inde-pendently in order to get optimized chiroptical effect. Wecarried out the period sweep of the supercell while keepingdimer distance unchanged within unit cell. The contourplot of the corresponding transmission and absorptionspectra (the upper andmiddle panels), as well as CD signal(the lower panel) for different periods are depicted inFigure 6. The RAs calculated from Equation (1) is super-imposed as dashed lines for comparison.

The ABDQ and BDQ modes are excited around,respectively, 840 and 940 nm, which are denoted by thered and blue arrows in the upper and middle panels ofFigure 6b. We therefore distinguish the period of supercellin three regions according to the relative position between(1, 0)sup RAs and LSPRs band. For lattice period800 nm < p < 950 nm, RAs intersect with LSPRs modes,resulting in strong SLR modes. In this case, BDQ mode iseffectively excited under RCP incidence. The CD responsetherefore gets enhanced and reaches maximum whenp = 890 nm. When the period of supercell is smaller than800nm, (1, 0)sup RAare shifted to far short-wavelength sideof LSPR modes. Therefore, their diffraction coupling is

relatively weak. For large lattice period (p > 950 nm), LSPRslies above (1, 0)sup RA and thus cannot oscillate collec-tively. On the contrary, LSPRs start to interact with (1, 1)supand (2, 0)sub higher order RAs. The solid lines in the upperpanel of Figure 7a represent the absorption spectra of asparse arraywith a large period (p = 1210 nm). Although thepronounced resonances are spectrally overlapped withhigher order RAs (the vertical dashed lines), it has littleeffect on LSPRs except a resonant blue-shift. The resonanceshift can be attributed to the effective mode volume over-lapping between neighboring SRR dimers, which is similarto the result in Figure 3b. In contrast, the absorption of thetwo resonances for the array is comparable with that of thesingle dimer (lower panel, Figure 7a). In other words, chi-roptical effects of these regions restores to uncouplingsituation. This behavior, again, can be explained by thenear-field distributions of the sparse array (Figure 7b,c)which are almost identical with that of the single dimersituation (Figure 2b,c).

2.4 Enhancing chiroptical effects withother metamolecules

Given the concept that SLRs and LSPRs can be tailoredindependently, it is possible to exploit SLRs as a universalapproach to enhance the chiroptical effects of LSPRs basedmetamaterials. A typical example is shown in Figure S6where gold stereo-SRR dimer arrays with spatial shift d = 0

Figure 6: (a) Transmission under RCP (upperpanel) and LCP (middle panel) incidences,as well as CD spectra (lower panel) for thestereo-SRR dimer arrays with differentperiods. (b) The corresponding RCP and LCPincidences absorption (upper and middlepanels), as well as CD in absorption (lowerpanel) spectra. The unit has been convertedinto absorption cross section (μm2) bymultiplying the area of the unit cell. Thedashed lines indicate RAs, and the blue andred arrows in Figure 6b denote the BDQ andABDQ resonances, respectively.

S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism 3425

can be strongly enhanced by adjusting the lattice spacing.In addition, here, we demonstrate the robustness of SLRsfrom a new chiral metamolecule, that is, the chiral quad-rumer. Figure 8a illustrates the schematic of a chiralquadrumer array composed of two sets of orthogonallycorner-stacked gold nanodisk dimers [46]. The quadrumerarray is chosen deliberately for the following two reasons.First, it is easier to fabricate such structure with the currentnanolithography method, and it is also possible to furtherenhance the chiral responses of more complex oligomercluster arrays [47–49]. Second, the intrinsic CD signal for asingle chiral quadrumer is extremely weak (Figure S7),especially compared with a single stereo-SRR dimer.Nevertheless, our numerical simulation result indicatesthat the quadrumer supercell array also exhibits strong CDresponses (solid line in the lower panel, Figure 8b). A dip-to-peak profile centered around 1250 nm is observed due tothe selective excitation of the hybridized longitudinal

resonances, that is, the antibonding (ABDD) and bonding(BDD) dipole-dipole resonances (inset of Figure 8a).Compared with single chiral quadrumer whose ensembleCD signal is smaller than 0.1 (dotted line, magnified by 5times for a better visualization), the positive CD peaklocated at 1320 nm is enhanced by 10 times. As shown inFigure S9, we also simulate the transmission spectra andcalculate corresponding transmission CD of these struc-tures under circular polarized illumination from thesubstrate side, which reveal slightly reduced CD valueswith negligible polarization conversion, thereby con-firming the presence of intrinsic chirality in these struc-tures [50]. The near-field distributions of LSPR modesshown in Figure S8 indicates that the CD peak (CD = –0.42) located at 1103 nm stems from the diffractioncoupling of ABDDmode by (1, 1)sub RA in the substrate. Inaddition, the sharp peak around 1320 nm is the (1, 0)supSLR mode by the diffraction coupling of the BDD mode in

Figure 7: CD responses of a sparse stereo-SRR dimer array. (a) Absorption spectra ofthe sparse array with p = 1210 nm for LCPand RCP incidences (upper panel), and thecorresponding CD in absorption spectrum(lower panel). The dotted lines in the upperpanel are the absorption spectra of a singledimer scaled by a factor of 4, the dotted linein the lower panel is the ensemble CD singlecalculated based on the single dimer, thevertical dashed lines denote the spectralpositions of several RAs, and the tick labelson the right side represent the convertedcross section values bymultiplying the areaof the unit cell. (b) Near-field enhancement(left panels) and charge (right panels)distributions of the ABDQ, and (c) BDQhybridized resonances for the sparse array.

3426 S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism

the superstrate. This coupling is even stronger than that ofthe ABDDmode, whose CD signal in transmission is about0.60. The CD peak centered at around 900 nm is thetransverse hybridized resonance and will not be dis-cussed in this work.

2.5 Dynamic tuning of transmission CD

One important nature of SLR, in general, is that its excita-tion efficiency depends dominantly on the spectral over-lapping between RAs and LSPRs. Considering the fact thatthe excitation of SLRs don't relying on index-matchingconditions, it is therefore envisioned that the chiropticalproperties of a given structure can be dynamicallycontrolled bymanipulate the frequency detuning of LSPRs,an approach that one can easily playwith bymodifying thesuperstrate's index such as flowing in different liquidmaterials [111], or integrated with a phase-change material

layer [70, 71]. This is of particularly advantageous forpractical applications such as polarization engineeringapproaches, polarization sensitive imaging, and stereodisplay technologies, where the geometry of functionalmaterials cannot be changed [69–71, 73–79]. For a quali-tative assessment, we simulated the CD response of chiralquadrumer array embedded in different superstrates, asshown in Figure 9. The corresponding transmission spectraof chiral quadrumer array under LCP and RCP incidencesare represented in Figure S10. As expected, the spectralpositions and intensities for both ABDD and BDD modesare strongly modified under different superstrate indexes.When the refractive index is small (nsup = 1.00), CD signalsare relatively weak, given by –0.18 and 0.26 for theABDD and BDDmodes, respectively (black line, Figure 9a).The intensities of both CD peaks increase with theincreasing refractive index, reaching a maximum valuewhen nsup = 1.50, where the CD in transmission are morethan one times stronger than that of nsup = 1.00 situation

Figure 8: Enhanced CD spectra from chiralgold quadrumer arrays. (a) Schematics ofthe quadrumer array organized in C4symmetry. The supercell parameters are:period p=850 nm, center distance betweentwo adjacent quadrumer in a unit celld = 430 nm, radius of the disk r = 80 nm,disk thickness t = 30 nm, gap size betweenthe two disks on the same layer h = 10 nm,separation between the upper and lowerlayer s = 50 nm, and refractive index of thesubstrate nsub = 1.80 and the superstratensup = 1.50. Inset: the plasmonhybridization scheme between thelongitudinal resonances of the two dimerson the upper and bottom layers. (b) Thetransmission (upper panel) spectra underRCP (blue lines) and LCP (red lines)incidences, and the corresponding CD intransmission of the array (solid line, lowerpanel). Inset: the charge distributions of thetwo CD peaks. The dotted line is theensemble CD in transmission calculatedbased on the single quadrumer byneglecting the coupling between unit cells(magnified by 5 times for a bettervisualization), and the vertical dashed linesdenote the spectral positions of RAs.

S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism 3427

(red line, Figure 9a). By further increasing nsup (>1.50), theintensities of the CD peaks start to decrease, where the CDin transmission with nsup = 2.00 are comparable with thatof nsup = 1.00 (cyan line, Figure 9a).

The transmission spectra under RCP and LCP in-cidences as well as CD spectra are depicted in Figure 9b.The dashed lines denote the spectral positions of the RAs,and the dotted lines in the lower panel of Figure 9b sche-matically show the evolution of ABDDandBDDmodes. TheRAs from the substrate stay unchanged with increasingnsup, whereas the LSPRs band and RAs from the superstrateshift to lower energies. Nevertheless, the RAs in thesuperstrate red shift more rapidly compared with that ofthe LSPRs. Therefore, when nsup is small enough (e. g.,nsup = 1.00), resonance band of the quadrumer locates faraway from the RAs. The corresponding SLRs cannot beeffectively excited, thereby leading to weak CD responses.When nsup increases, the ABDD and BDD modes start tointersect with (1, 1)sub and (1, 0)sup RAs, respectively. In thiscase, strong diffraction coupling takes place between

nearby unit cells, yielding enhanced CD responses. Afurther increase in refractive index (nsup > 1.50) separate theLSPRs band and RAs again, which is the reason ofdecreasing CD responses. Interestingly, the sign of CDsignals can be switched progressively around the spectralposition marked with yellow bars in Figure 9a, whichmeans that the quadrumer array has flipped into “oppositeenantiomer” simply by changing its cover materials.

2.6 Modified Born–Kuhn model

The modified plasmonic Born–Kuhn model can be used todescribe the underlying physics for the SLR-enhanced chi-roptical response. The plasmonic Born–Kuhn model hasfound tremendous success in explaining the plasmonicchiroptical effects [11, 46], where the optical activity ofplasmonic chiralmaterials canbe interpretedas the couplingbetween two oscillators resonating perpendicularly to eachother. The schematic is shown in the inset of Figure 10,where

Figure 9: Dynamic tuning of CD responses. (a) The CD spectra in transmission under different superstrate indexes for the same chiral quadrumerarray, where the sign of CD signal is switched around the spectral positionsmarked with yellow bars. (b) Transmission spectra under RCP (upperpanel) and LCP (middle panel) incidences, as well as the CD responses (lower panel) for the quadrumer array under different superstrate indexes.The dashed lines show the spectral position of RAs, and the dotted lines in the lower panel denote the evolution of ABDD and BDD modes.

3428 S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism

a yellow oscillator (u1 = A1e–iωt) is placed at the upper layer

and a blue oscillator (u2 = A2e–iωt) is located at the bottom

layer. In the modified Born–Kuhn model, each oscillatorrepresents the collective SLR modes of top (bottom) reso-nance layer only. This treatment is a naturalway ofmodelinglongitudinal propagating resonances as the upper (lower)nanostructure layer plays, respectively, the dominate rolewhen the RAs of the superstrate (substrate) are involved inthe formation of SLRs. The coupling between the superstrate(substrate) RAs with the opposite side of layer is neglected.As a result, these oscillators inherit from the basic propertiesof RAs such as non-resonant features and independentspectral position determined only by surrounding materialsthemselves. In this way, the two collective resonances areindependent. The damping of the collective resonanceswould be weaker than that of the localized resonances.

As a result, the dynamic equation of the SLR-enhancedchiral metamaterial responding to circularly polarizedwaves is given by the following Lorentzian equations oftwo coupled oscillators [46],

[ω21 − ω2 − iωγ1 κ12

κ12 ω22 − ω2 − iωγ2

][A1

A2] � −[g1Eyeik(z−s/2)

g2Exeik(z+s/2)](2)

where ω1(2) denotes the resonance frequency, γ1(2) is thedamping of the corresponding oscillator, κ12 is the couplingstrength of the two oscillators, s is the vertical distancebetween the two dimers, and g1(2) denotes the coupling

strength of the oscillator with the incident field. The CDresponses are related to the nonlocality tensor Г(ω) [112],and one can get an analytical expression of the CD intransmission with a detailed derivation shown in themethod section [46],

ΔT � TRCP − TLCP

� 4ω2

2c2Im

⎧⎪⎪⎨⎪⎪⎩4πeN0sg1g2

κ12ω2

2 − ω2 − iωγ2

(ω21 − ω2 − iωγ1) − κ212

ω22 − ω2 − iωγ2

⎫⎪⎪⎬⎪⎪⎭(3)

where N0 is the charge carrier density. Equation (3) formsthe central result of the modified Born–Kuhn model andagrees well with the simulation spectra from thequadrumer array, as shown in Figure 10. In addition, ithas been shown that the diffraction coupling in thesuperstrate is stronger than that of the substrate, and thefitted result, indeed, reveals that the damping of the upperoscillator that embedded in the superstrate is weaker thanthat of the lower one in the substrate (γ1 < γ2), indicating amore effectively coupling with the RA in the superstrate,and the intensity of the positive CD peak is stronger thanthat of the negative one. Note that, in addition to thelongitudinally hybridized resonance considered in theBorn–Kuhn model, the transversely hybridized resonancefor the upper and lower nanodisk dimers leads to the chiralresonance at around 900 nm, which explains thedifference between the FDTD calculation and the Born–Kuhn model results in this spectral range.

3 Conclusion

In conclusion, we have shown that the excitation of SLRscan significantly enhance the chiroptical response ofplasmonic metamaterials up to 10 times, with a maximumof CD around 0.7. For a matched circularly polarized inci-dence, the diffraction coupling between an LSPR and RAsresults in strong optical interactions, thereby leading to anamplified absorption. As a result, enhanced CD responsescan be achieved simply by choosing a proper period of thearray even though the intrinsic chirality of constitutionalmetamolecules is small. In addition, SLRs and LSPRs aretwo robust plasmonic effects with distinct underlyingphysics. Their combination showcases a new degree offreedom to design plasmonic chiral nanostructures. As ademonstration, the phenomenon of “chirality inversion” isobserved in the chiral quadrumer arrays simply by

Figure 10: Comparison between the calculated CD in transmission(circular points) and the fitted spectra from the Born–Kuhn model(solid line) for the chiral quadrumer array shown in Figure 8. Inset:the plasmonic Bohn–Kuhn model with only the longitudinalresonances of the upper and bottom layers are considered. Thefitting parameters are ω01 = 242.84 THz, ω02 = 258.20 THz,γ1 = 3.65 × 1012 s–1, γ2 = 2.28 × 1013 s–1, and κ12 = 1.08 × 1028 s–2.

S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism 3429

changing its cover materials. Although this works focuseson the physics of SLR enhanced plasmonic chirality, theproposed structures can be readily fabricated by the cur-rent state-of-the-art nanofabrication techniques, e. g., two-step electron-beam lithography. This technique has beenused to successfully fabricate stacked metasurfaces,including stacked split-ring resonator [89], corner-stackedgold nanorods [11], and twisted metamaterial [15, 113]. Ourapproach could be beneficial in the following two aspect.First, the enhanced CD peaks inherit from the propagationproperty of SLRs, that is, sharp resonance peaks with highQ-factors, which is a priori for practical applications suchas biosensing andpolarizationmanipulation [114]. Second,the spectral position of RAs can be dynamically tuned bysuperstrate, thereby leading to the active control of mate-rial chirality. Considering that a propagating SLR modedoes not process any chiral properties, it is counterintuitivethat the SLR can be used to enhance chirality. Therefore,our resultswill open the door to novel plasmonic designs ina wide range of applications, which will definitely findapplications in broader areas.

4 Methods

Electromagnetic Simulation: The finite-difference time-domainmethod was used to simulate the optical responses of the singleplasmonic nanostructure and the supercell arrays. The dielectricconstants of gold were taken from literature [115]. A normal incidentpulse along the –z direction was used as the excitation source.Perfectly matched layers were set at all sides as the boundaries forsingle nanostructures simulation, while periodic boundary conditionwas imposed in x- and y-directions, and PMLs were set at the top andbottom for supercell simulation.

Born–Kuhn model: From the Lorentzian equations that describingthe motion of the two coupled oscillators (Equation (2)), one can getthe amplitudes of the two oscillators [46],

A1 � −g1Eye−iks/2 −

κ12g2

ω22 − ω2 − iωγ2

Exeiks/2

ω21 − ω2 − iωγ1 −

κ212ω2

2 − ω2 − iωγ2

eikz (4)

A2 � −g2Exeik(z+s/2) − κ12A1

ω22 − ω2 − iωγ2

(5)

Suppose that the charge and the velocity of an electron are, respec-tively, –e and v, the current density at a point r can be written as J(r) =–evδ(r), and the total current density can be calculated as,

Jx � −eN0g2du2dt

(6)

Jy � −eN0g1du1dt

(7)

where N0 is the charge carrier density, and Jz = 0. Since the polari-zation P(ω, r) = J(ω, r)/(–iω), one can get the nonzero polarizationcomponents,

Px � eN0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣ g22ω2

2 − ω2 − iωγ2Ex

−

κ12g2

ω22 − ω2 − iωγ2

g1Eye−iks − ( κ12g2ω2

2 − ω2 − iωγ2)2

Ex

ω21 − ω2 − iωγ1 −

κ212ω2

2 − ω2 − iωγ2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦eikz(8)

Py � eN0⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣ g21Ey −

κ12g2ω2

2 − ω2 − iωγ2g1Exeiks

ω21 − ω2 − iωγ1 −

κ212ω2

2 − ω2 − iωγ2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦eikz (9)

where the approximation e±iks ≈ 1 ± iks has been used. The first-orderapproximation of the linear constitutive equation can be used todeduce the nonlocality tensor,

Pi(ω) � 14π

{ ∑j�x,y,z

[εij(ω) − δij]Ei(ω) + ∑j�x,y,z

∑n�x,y,z

Γijn(ω) ∂Ej(ω)∂rn

} (10)

where εij is the material permittivity tensor, Гijn is the material non-locality tensor, and δij is the Kronecker delta symbol. Then, one canobtain the nonzero components of the nonlocality tensor bycomparing Equations (8) and (9) with Equation (10),

Γxyz � −Γyxz � 4πeN0s

κ12g2ω2

2 − ω2 − iωγ2g1

ω21 − ω2 − iωγ1 −

κ212ω2

2 − ω2 − iωγ2

(11)

By considering the propagation direction in an isotropic medium, onecan get,

Γ � Γxyz (12)

The ellipticity of the propagation wave per length unit can be writtenas [112],

sin 2η � tanh[ω2

c2Im{Γ}] (13)

where the first-order approximation can be used since η « 1,

η � ω2

2c2Im{Γ} (14)

The ellipticity and transmission for LCP and RCP incidences fulfills thefollowing relation,

tan η �����TRCP

√−

����TLCP

√����TRCP

√ + ����TLCP

√ (15)

Considering that η « 1, one can obtain,

η � (TRCP − TLCP)/4 (16)

By substituting Equation (14) to Equation (16), one can get theanalytical expression of the CD in transmission (Equation 3), which isused to fit the simulated spectrum to obtain the properties of indi-vidual oscillators [46].

3430 S.-D. Liu et al.: Dynamic tuning of enhanced intrinsic circular dichroism

Acknowledgment: This work was supported by the Na-tional Natural Science Foundation of China (NSFC)(11874276 and 11574228), the Research Grants Council ofHongKong (CRFGrant No. C6013-18G), the San Jin ScholarsProgram of Shanxi Province, and the Key Research andDevelopment Programof Shanxi Province (201903D121131).

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Supplementary Material: The online version of this article offerssupplementary material https://doi.org/10.1515/nanoph-2020-0130.

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